Corrie bought a new flat screen 70 inch television and a speaker system from a l
ID: 2895755 • Letter: C
Question
Corrie bought a new flat screen 70 inch television and a speaker system from a local electronics store on credit. The store will charge 12% per year compounded monthly. Their monthly payments are $174.80 for 3 years. What is the cash price of her purchase? Identify the tvpe of problem a. Future Value with compound interest b. Present Value with compound interest c. Present Value of an Annuity d. Future Value of an Annuitv e, Future Value with simple interest Answer the question in the problem a. $4,881.98 b. $5,262.79 c. $4,956.80 d. $3,762.26 e. $4,382.98Explanation / Answer
The problem asks us the cash price of Corrie's purchase its the same as the present value of an annuity.
An annuity is a fixed amount which is paid over a given period of time.
(c) Present value of an annuity.
The present value is the current value of a group of values paid in the future. The group of future values come at an interest or discounted rate.HIgher the discount rate, lower would be the present value.
The present value of an ordinary annuity is given as
Present value = C*[1 - (1+i)^(-n)]/i
C = amount of payment per period
i = interest rate
n = number of payments
In our problem
C = $ 174.80
i = 12% per year compounded monthly = 12/(12*100) = .01
n = 3*12 = 36
= Present Value = 174.80*[1 - (1+.01)^(-36)]/.01 = $ 5262.791
Option (b) is correct